English
Maps bounded formulas along a pair of term and relation transforms, producing a new bounded formula whose shape is obtained by applying these transforms to the corresponding components.
Русский
Отображение ограниченной формулы через преобразования термов и 관계, дающее новую ограниченную формулу.
LaTeX
$$$\text{mapTermRel} : (ft)→(fr)→(h)\; ∀ φ,\; φ.mapTermRel ft fr h ∈ L'.BoundedFormula β (g n).$$$
Lean4
/-- Maps bounded formulas along a map of terms and a map of relations. -/
def mapTermRel {g : ℕ → ℕ} (ft : ∀ n, L.Term (α ⊕ (Fin n)) → L'.Term (β ⊕ (Fin (g n))))
(fr : ∀ n, L.Relations n → L'.Relations n)
(h : ∀ n, L'.BoundedFormula β (g (n + 1)) → L'.BoundedFormula β (g n + 1)) :
∀ {n}, L.BoundedFormula α n → L'.BoundedFormula β (g n)
| _n, falsum => falsum
| _n, equal t₁ t₂ => equal (ft _ t₁) (ft _ t₂)
| _n, rel R ts => rel (fr _ R) fun i => ft _ (ts i)
| _n, imp φ₁ φ₂ => (φ₁.mapTermRel ft fr h).imp (φ₂.mapTermRel ft fr h)
| n, all φ => (h n (φ.mapTermRel ft fr h)).all
